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Complementary Angles — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSComplementary Angles2 Marks
Question
Evaluate $: \sec^2 18^\circ - cosec^2 72^\circ$
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Answer

$\sec^2 18^\circ - \operatorname{cosec}^2 72^\circ$
$= [\sec (90^\circ - 72^\circ)]^2 - \operatorname{cosec}^272^\circ$
$= \operatorname{cosec}^2 72^\circ - \operatorname{cosec}^2 72^\circ$
$= 0$

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